Engineering tools

Spring Rate Calculator — Guide

Compression, extension and torsion springs — inputs, material selection, spring index, stress checks and worked examples for all three types.

What this calculator covers

The spring rate calculator uses the standard Wahl-corrected formulas for all three common spring configurations. Each is accessed via its own tab — the inputs change depending on the spring type, but the underlying approach is consistent: enter the wire and coil geometry, select a material, optionally enter a load or moment to check deflection and stress.

Note on scope: this calculator gives spring rate, stress and deflection for a given geometry. It doesn't design the spring from scratch or optimise for a given rate — you need to supply the geometry and it tells you what that geometry produces.

Material selection

Selecting a material from the dropdown auto-fills three fields: the shear modulus G (for compression/extension) or elastic modulus E (for torsion), and the allowable stress default. These fields are locked while a real material is selected — they turn grey and can't be edited, so it's clear that the calculator is using the material's values rather than whatever was previously in the box. Switching to Custom unlocks all three fields for manual entry.

The allowable stress values are typical mid-range defaults for each material — they vary with wire diameter, temper, and application. For a real design, always check against your supplier's datasheet or the relevant standard (BS EN 10270, ASTM A228, etc.) for the actual wire size you're using.

Material	G (GPa)	E (GPa)	Typical τ_allow (MPa)
Music Wire (ASTM A228)	79.3	207	620
Hard Drawn Steel (A227)	79.3	207	450
Oil Tempered (A229)	79.3	207	480
Chrome Silicon (A401)	79.3	207	620
Chrome Vanadium (A232)	79.3	207	550
Stainless 302/304	69.0	193	480
Stainless 17-7 PH	75.8	203	620
Phosphor Bronze	41.4	103	280
Beryllium Copper	44.8	124	340

Spring index and the Wahl correction factor

The spring index C = D/d (mean coil diameter divided by wire diameter) is shown in the results alongside the Wahl correction factor K_w. The Wahl factor accounts for the stress concentration effect at the inner surface of the coil — a tighter coil (lower C) has a higher stress concentration than a looser one. The calculator applies this correction automatically to the stress result.

The calculator flags spring index values outside the normal 4–12 range:

C below 4 — difficult to form, very high inner-surface stress concentration, tooling wears quickly. Review the design.
C above 12 — coil is likely to be unstable, prone to tangling in bulk storage and handling. Review the design.

Compression spring — inputs and worked example

Field	Meaning
Wire diameter, d	Wire cross-section diameter in mm
Mean coil diameter, D	Diameter measured to the centreline of the wire — not OD or ID
Active coils, N_a	Number of coils that actually deflect — excludes closed/ground end coils
Shear modulus, G	Auto-filled from material; use Custom to enter manually
Applied force, F (optional)	Force in N to calculate deflection and check stress against allowable

Worked example — compression

d = 2.00mm, D = 16.00mm, N_a = 8, Music Wire (G = 79.3 GPa), F = 50N

Result	Value
Spring rate k	4.840 N/mm
Spring index C = D/d	8.0 ✓ within normal range
Wahl factor K_w	1.184
Deflection at 50N	10.330 mm
Shear stress at 50N	301.5 MPa ✓ below 620 MPa allowable

Formula: k = G·d⁴ / (8·D³·N_a)

Extension spring — inputs and worked example

Extension springs share the same rate formula as compression springs. The additional field is Initial tension F_i — the built-in pre-load that must be overcome before the spring begins to extend. Deflection is calculated from the force in excess of F_i; the stress check uses the full applied force F.

If the applied force F is at or below initial tension F_i, the calculator flags that the spring hasn't yet started extending — the coils are still closed and the spring isn't deflecting.

Worked example — extension

d = 1.50mm, D = 12.00mm, N_a = 10, Music Wire, F_i = 5N, F = 40N

Result	Value
Spring rate k	5.565 N/mm
Spring index C	8.0 ✓
Extension beyond F_i	(40 − 5) / 5.565 = 6.290 mm
Shear stress at F = 40N	checked against allowable

Torsion spring — inputs and worked example

Despite the name, torsion springs work in bending, not torsion — the wire bends as the spring winds or unwinds. The rate is in N·mm per revolution (and per radian), and the stress check uses a bending stress correction factor K_b rather than the Wahl shear factor. The elastic modulus E is used rather than the shear modulus G.

Field	Meaning
Applied moment, M	Torque applied to the spring in N·mm
Allowable bending stress	Higher than the shear allowable for the same material — torsion springs work in bending

Worked example — torsion

d = 2.00mm, D = 18.00mm, N_a = 6, Music Wire (E = 207 GPa), M = 500 N·mm

Result	Value
Rate k	2743 N·mm/rev (436.6 N·mm/rad)
Spring index C	9.0 ✓
Bending factor K_b	1.090
Rotation at M = 500 N·mm	65.6°
Bending stress	694 MPa — check against your material's allowable bending stress

Formula: k = E·d⁴ / (10.8·D·N_a) N·mm/rev

Disclaimer

This calculator is provided free of charge and on an as-is basis, with no warranty or guarantee of accuracy, fitness for purpose, or suitability for any specific application. Material properties are typical mid-range values — always verify against your actual wire specification before relying on stress results for a real design.

AbarTech Ltd accepts no liability for any outcome arising from use of this tool. Results are a starting point for design, not a substitute for proper engineering analysis, testing, or qualification.

If you'd like engineering support on a specific spring design, get in touch.